Sunday, December 01, 2013
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The comet has been doomed at least since the first moment when it looked so; claims to the contrary were always just some irrational religion

The good folks who were excited about the alleged resurrection of Jesus Christ were not too unreasonable. To say the least, they were not more unreasonable than most science writers who were producing stories about comet ISON's "survival" in recent days.

When I wrote the satire about the comet's destruction by global warming (yes, there were some readers who didn't understand it was a satire!), I took one claim for granted: the comet couldn't have survived, at least not to the extent needed for the comet to be visible by the naked eye e.g. today and the visibility of ISON's remains would be guaranteed to decrease quickly.

(The debris had magnitude plus 7 late yesterday which already made it invisible. NASA's JPL predicted a year ago that the brightness of the comet could be around minus 11.6 by now, brighter than the full Moon. That prediction has failed rather spectacularly, hasn't it?)

But you must have seen reports by pretty much everyone – Fox News, The Guardian, Matt Strassler, and thousands of others – who were completely excited with their thoroughly unjustified claims that the "comet has survived", "we have a hope", and so on – the similarity of ISON with Son of God is almost perfect.

Let's restore just some common sense and elementary physics.

On November 28th, the comet approached the perihelium, the closest point to the Sun on its trajectory. Its distance from the Sun was just a little bit larger than 0.01 AU – AU is the distance between the Earth and the Sun. It was almost 100 times shorter than the Earth-Sun distance. Perhaps 0.015 AU, I forgot the exact number.

Fine. The amount of "watts per squared meter" that you're getting from the Sun depends on the distance as \(1/R^2\) – the photons just get spread over the sphere of radius \(4\pi R^2\), if you wish. So the number of "watts per squared meter" is approximately \(10,000\) times greater at the point of the comet's perihelion than it is here on Earth.

However, the equilibrium temperature is one at which the outgoing thermal radiation matches the incoming one. The outgoing thermal radiation goes like \(T^4\) so the equilibrium absolute temperature \(T\) "over there" is about \(10\) times greater than it is on Earth because \(10^4=10,000\). On Earth, it is something like 300 kelvins (the room temperature or so) which means that you expect the temperature on the comet as it approaches this perihelion to go to several thousand of degrees.

What can be burned near the surface will burn – and become darker in color (think of burned wood). All the ice and water will surely vaporize. At these high temperatures, the water beneath the surface of any "ice core" is moving somewhat frantically and the heat quickly gets deeper inside the comet. Any hole means that all the ice and liquid water vaporizes and gets away.

So what you see when the comet gets this close to the Sun is just some heated material that radiates but the material that has a chance to hold together is nearly black and the remaining material is mostly vaporized which means that the molecules are moving away from others.

Water, ice, and some thin atmosphere are important for the visibility of a comet. It is not hard to see that the atmosphere has no chance to survive the heat. Take the Halley comet whose numbers haven't become obsolete because of the comet's death. Its diameter is of order 10 kilometers. This chunk of mass has some gravitational field but it is tiny. It's more meaningful to talk about the escape velocity from the Halley comet. You know how much it is for similar masses? It is 2 meters per second. If a gas molecule moves faster than 2 meters per second, it will never return. Compare this escape velocity with 11,000 meters per second from the Earth, a large enough value so that NASA needs to use rockets to escape the Earth's gravitational pull.

The escape velocity of 2 meters per second is so tiny that slightly heated gas instantly escapes. To understand this point, realize that at the room temperature (the equilibrium temperature near the Earth, approximately), the average speed of an air molecule is around 500 m/s. Now, the kinetic energy is proportional to the temperature (\(3kT/2\) etc.) so the speed is only proportional to the square root of the absolute temperature. I said that the absolute temperature may be around 10 times greater on the comet while near perihelion so the average speed of gas molecules over there will exceed 1,000 m/s. It's much greater than the escape velocity from the comet's very weak gravitational field.

So the cute coma is not really bound to the comet once it gets heated up. The gas molecules' speed is vastly higher than the required escape speed and the gas will just tell the comet good-bye, forever.

One could discuss some solid materials that have a chance not to vaporize. Some pure metals could arguably melt and refreeze later. If that happened, the comet could become a mirror which doesn't really reflect much light to generic directions. I won't probably happen, anyway. More likely, one may get some solid leftover material that is dark – and therefore absorbs lots of radiation, with the risk of evaporating earlier. And even if this dark material doesn't evaporate, it won't be visible.

Birth of Jesus Christ, Israel, 2017 years ago

There are obvious reasons why the "nearly compact" heated up material is visible when it is so close to the Sun: it is strongly illuminated by the nearby Sun and it is also producing its own heat and thermal radiation. However, at these high temperatures, there is no good reason to think that a light-colored non-gaseous material will survive anywhere near the comet's surface. Even if the comet (comet ISON's diameter is about 5 kilometers) were large enough to preserve a big chunk of ice etc., it will be hidden "inside" the dark material. The side that is close enough to the Sun – and it's the only side we can see by the naked eyes when the comet cools down again – has been darkened and/or vaporized.

That's the "complicated reason" why I found the hype about the resurrection and befuddled experts to be simply stupid. Sorry, Matt, your excitement lacked common sense and the comments that "experts are befuddled as well" is a lame excuse.

But there's one "simpler reason" why I found the reports really stupid. Comet ISON has already been seen to have largely disappeared. Well, this is like the process of dying and this process is, as you may have heard, pretty much irreversible. If the "health" of the comet looks somewhat better than an hour ago, it may be just a coincidence (a more reflective side of the debris was just rotated in the right direction or whatever). But to expect the comet to reappear in its original strength is exactly as naive as to expect a human being or Jesus Christ to be resurrected – apologies to the Christians who may think it is not naive. It violates the second law of thermodynamics and such violations are statistically allowed but only if they're "small".

Note that some comets in the empty space have no problems with the escape velocity etc. The temperature of outer space (its cosmic microwave background) is around 2 kelvins which is 100+ times lower than the room temperature (on Earth). That makes the thermal speed about 10 times smaller, comparable to dozens of meters per second, and some heavy comets may be able to beat it. (And the Halley comet distance at the perihelion is 0.6 AU, so the conditions on the comet are never too different from those on the Earth.)

You might also ask why it is that exactly "now", comet ISON died. Such comets exist for billions of years so why now? Well, there probably used to be many more comets at the beginning. Their number is dying away.

For exactly elliptical orbits, it would be very unlikely or impossible for the comet to approach very close to the Sun if it didn't do during its previous perihelion (the elliptical orbits are periodic). But I guess that there is some friction that reduces the velocity of the comet. For the "radial" direction, this doesn't matter much because the radial velocity is increased by the Sun's gravity again. However, no one is "restoring" the transverse, angular components of the velocity, which is why the comets' impact parameter is probably continuously increasing (along with the eccentricity); their speed is getting directed in the radial direction, making it increasingly likely that they will hit the Sun ("be sucked by the Sun") or its vicinity.

You may be sad but please forget about resurrection: Whatever material is left out of comet ISON will never look like a sexy hairy shining babe again, especially not to your naked eyes. The comet was visible shortly after it was doomed because it was heated by the nearby Sun and it was strongly illuminated by the nearby Sun. But already now, the distance of the comet from the Sun has increased 10 times relatively to the perihelion and as the distance continues to increase, the illumination by the Sun will go down much like the comet's temperature and the chance to see it with naked eyes will plummet to zero (from the already hopeless current values).

(BTW I was also close to writing something stupid about the comet. On Tuesday afternoon, before 5 pm or so, I saw Sirius which seemed brighter than I remembered it. Before I got home, I was convinced it had to be ISON. I even wrote two quick e-mails and 6 lines of a prepared blog post about the happy experience. But then I quickly got back to my senses, realizing that the location, timing, and shape were all wrong, and I wouldn't be trying to hide for a second that I was being stupid for half an hour. But some people are being stupid for days if not years or decades and they're trying to hide their stupidity in elaborate ways which is bad.)

snail feedback (38)
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Water. When is it visible? Clearly you can see ice. However you can't see steam, its transparent. Once condensed, you can see it again. Is the lack of a tail a result of the water being steam, and not condensing out into a mist?

Secondly, I hear lots about the comet being a means of determining the state of the primordial solar system. However, its on a hyperbolic trajectory. What evidence is there that it comes from our solar system, and isn't a visitor from another solar system? It's odd that its a sun grazer. If it was in orbit around the sun, to come into the inner solar system then it can't have had much angular momentum. It would need a large mass to divert it into the centre. Seems odd to me.

in your finite human mind,resurection is not possible.But with God who is the creator of your finite mind and everything in the univrerse,anything is possible.Jesus lives because he is God in the flesh,he created men from the dust of the Earth.He surely can resurrect a dead body.He SPOKE everything into xistance,Praise Jesus !!!!!!!

Creation and annihilation operators and path integrals go beautifully hand on hand together and not just as alternative options, see Faddeev&Slanov book on gauge fields and Xiao-Gang Wen book on Quantum field theory of many body systems

Mr Motl I agree with you that energy conservation is not valid all around the known universe, but as you say that since energy conservation is simply invalid and then any physical process can generate energy then why are perpetual motion machines mocked on ?

I think being able to reproduce the (relevant) results one wants to generalize, apply to new systems or situations, etc is a necessary prerequisite to ensure that one knows what one is doing in new research. Feynman is exactly right !

And it is not true that good theoretical physicists, who are very strong in formal work for example, have a deficite concerning language issues. On the contrary, I have observed that they have the most clear way of thinking and writing when explaining or presenting stuff, use technical terms and definitions consitstently (conversely to the situation in softer sciences), and avoid unnecessary babbling and creating impenetrable fogs (what people who dont know what they are talking about often do, compere for example high- and low-level questions on Physics SE...), but often have an immensely cool nice sense of humor that makes one rolling on the floor ;-)

When being interested in applications of renormalization group ideas to turbulence, I immediately liked the ERG (or functional renormalization group) appoach, which seems to be much more general, much better that the method introduced by Orszag et al. which relies on many approximations, does not allow for operators or interactions to become (ir)relevant in the course of the RG flow, etc ... :-P.

And it is slightly regrattable, that Zweibach said right at the beginning that he will use no path integrals in his book ...

This is Kavan writing you. I am a student at the univ of Virginia. I had the pleasure to read your answers on physics forums about the concept of a photon interfering with itself. Very good.I know this space is for comments on ISON but I could not find your email to contact you.I would like to ask you some very basic questions on the topic. Let me know if you have some time and i will email you my queries. Best regards,Kavan

Dear Rijul, it is mocked because in the Earth-like conditions, the spacetime is nearly flat and the energy conservation holds almost accurately.

Almost equivalently, the time needed to change the energy by 100 percent or so due to the cosmological nonconservation is of order 10 bilion light years so it is not a fast enough or practical way to produce energy for free.

ISON perihelion was ~250 miles/sec. If the sun were cold monoatomic hydrogen, that most probable relative velocity gives a temp around 8 million K. Warm. However, the comet is belching insulating vapor re the Ledenfrost effect. It also has a blunt leading shock wave reflecting much of the nastiness, re space capsule heat shields. Complicated,

Important are its Roche radius and compression strength re the leading shock. We know ISON has lots of carbon for its Swan line green coma, radiating acetylene and cyanide radicals. ISON will do what ISON does based upon its unknown chemical and physical material properties.

Grant funding by managers requires scientists to be streetwalkers showing thigh all the way up, and promising so much more with zero risk and large DCF/ROI, all of it locked into a PERT chart. The best funding strategy is for a department to, by lottery, assign asinine extreme predictions to its faculty for publicity. Somebody is sure to hit, get funded, then intramurally share the wealth.

Dear Uncle Al, it is physically meaningless to compare the speed of celestial bodies with the thermal speed of gas molecules. The thermal motion has random directions and signs so one may always distinguish it from the collective motion of whole celestial bodies and these two types of contributions to a molecule's motion never mix.

There are billions of icy objects in the Kuiper Belt, which lies beyond Neptune and out to about 50 AU. Some are very large, such as the planetismal, Pluto, and some are very small. They are relics of the formation of the solar system and, therefore, represent the original makeup of the material that condensed to form that system. Complex gravitational interactions cause some of them to be ejected into interstellar space and a very few are directed toward the sun. We call these comets.

I'm quite aware of the mechanism. However, even in the Oort cloud they are in an orbit. To get them to become a sun grazer needs them to make a 90 degree turn. and effectively go into free fall. That's strikes me as very unlikely. Particularly for ISON which is on a once only trip in. Hyperbolic orbit.

They started advertising the special presentation, Super Comet ISON 2013, [Saturday, Dec. 7 at 10 p.m. ET/PT on Science Channel] during Thanksgiving.

Filled to the brim with hope for comet resurrection, with descrete commercial interruption. I'll be expecting Chevron to remind us all that they really dig windmill power, which is in no way to be construed to mean that they are chrony capitalist suck ups to the regulation state.

Inconvenient comets may evaporate, but overhyped TV events are eternal.

Molten dark metal residue would result in Widmanstätten pattern meteorites, I think.

I agree with most of your blog post, but it is a stretch to say that one shouldn't care about other methods if one's own method works. Obviously there are potential upsides to becoming comfortable with another method, not just familiar, because perhaps it isn't clear at first that it is inferior or superior to your own way.

HEALTH WARNING: I'm not a physicist so this might the a dumb question.

I know the standard calculation for getting the Earth's steady-state average temperature, (with tweaking for its albedo) from the Sun's output using Stefan's law and the need to invoke the greenhouse-gas' mechanism to explain the temperature difference. It hinges on taking the insolation on a disc the same diameter as the earth and then simply averaging that over the whole surface of the Earth (four times larger).

I wondered if that averaging were a little too simplistic. What I'm think is that if the difference between average day- and night-time temperatures were (I'm guessing for argument's sake) 20K then the rate of emission from the Earth would vary by a factor on the order of ~(1+20/300)^4-1, i.e. about 30% between day and night. Which means, in round terms, losing heat at a 30% lower rate at night than during the day with possible(?) implications for the resulting calculated steady-state temperature.

Ignoring the GHG effect, albedo and any other complications for the moment, and taking the Earth as say a thin (pick a depth) copper* spherical shell painted matt black (i.e. a black body), then knowing its thermal conductivity and capacity at every point it should be a straightforward matter to do the integrations and whatnot to arrive at the temperature at time t (modulo 24 hours) for all points on the surface. It isn't obvious to me then whether the resulting average temperature over the Earth's whole surface (necessarily the same for all times t, assuming a steady state) would be the same as that given by the standard calculation. Maybe it should be and I'm about to have a doh! moment thrust upon me, but it isn't.

Does anyone know of such a calculation and its results? Or is there an 'obvious' way one can see this would give the same result as the regular calculation?

* It doesn't have to be copper. Anything will do as long as its properties are nicely behaved for model purposes. Water would be best I suppose as it covers 2/3rds of the surface (ignoring oceanic currents as a first approximation).

Prof. Hsu wouldn't have given his young student Feynman an A, that's for sure. Of course Hsu is totally hung up on the subject of "intelligence" as "g," the underlying correlate of various mental abilities. Feynman only cared about the pudding.

In some sense, even Clifford Johnson who loves to be in the top 5% of the "drawing scientists" is just emulating Feynman.

I would like to see Steve's paintings of women - or the arts by other folks who love to pompously present themselves as versatile, cultural men. Most of their image is just empty and offensive postmodern smugness.

1.. Did you mean billions of years ? Light year is a unit of distance not time2. What I meant to say is that if someone formulates a concept in which he happenes to find little output energy without input, can it be simply explained by saying that conservation of energy is not exactly correct and is more of an approximation, hence it is ok if some energy is being created in proposed process ?

1. Yes, it's billions of years - in the c=1 units, a year and a light year is the same thing and I implicitly use the units all the time. The same comment may be rephrased to space. The typical "size of the region" you need to change the energy by O(100 percent) is of order tens of billions light years, too.

2. No, you cannot ever violate the energy conservation law unless you are considering a situation in which the whole global shape of the Universe - its asymptotic behavior at infinite distance - is being transformed. So whatever happens near the Earth will always conserve the energy pretty much exactly, with the deviations' being undetectable. I have already explained that.

You just ignore the answer because you seem obsessed with the idea that the invalidity of the energy conservation law in general cosmology justifies perpetual motion machines on the Earth. It doesn't, not even an iota of a justification.

I have just one more question for now, why are you and most (not all) people so adamant that noone can violate the law of conservation of energy, many places I have read that law of conservation of energy is just a law that has not been violated untill now, it was also said that to satisfy the law classical energy had to be redefined to support mass energy conversion. So my question is why so much of certainty that the law cannot be broken (for earthly or other simple matters) when we can modify basically everything we know and classify them as quantum and classical, why is someone thought of as a fool if he says that, Yes ! it it possible, not impossible.

Dear Rijul, it is impossible, not possible, to violate the energy conservation law in this Universe in all situations in which the overall cosmological time-dependent curvature of the Universe may be neglected or plays no role.

The energy conservation law has been shown to be equivalent to the time-translational symmetry of the laws of physics. That's Noether's theorem. Both versions of the law/symmetry are natural and agree with every single observation, arbitrarily accurate one, that has ever been made and every single fundamental or effective law to describe Nature that has ever been extracted from the observations.

That's why people who think that they may violate the energy conservation law in ordinary conditions are imbeciles in the denial of reality, to put it very diplomatically.

Not the temperature of the *comet* from its speed, but the apparent kinetic temperature of an impinging gas molecule upon the comet. De Laval nozzle vacuum-expanded molecular beams have rotational temps hard by absolute zero. In the lab frame they are supersonic (though Mach 1 in vacuum is much lower than 340 m/s for an unremarkable local Mach 20 beam).

Dear John,the right calculation of the Earth's equilibrium temperature deals with average (or total) energy flows.

It's really simple to know what's the average solar energy coming to Earth from all directions, averaged over all places, daytime, and seasons.

You want this average inflow of energy to be "per unit of area of the Earth's surface". The area of a sphere is 4.pi.R^2. But the radiation is really hitting the "cross section" which is a disk of area pi.R^2. So you just divide 1340 watts per meter squared by 4 to see how much the Earth is absorbing in average. This does all the three averagings automatically and exactly.

Thank you very much for taking the time to reply. I appreciate it, especially as this is kindergarten-level stuff for you.

"Of course, one may do a more accurate calculation including the profiles and albedos."

Actually, that's (kind of) what I meant. But I also wanted to eliminate complications like albedo as what I was driving at was what I thought was the rather simplistic approach specifically taken to this averaging itself in the standard calculation. And yes, I appreciate that it's the energy flows that are the central issue here (actually that's what I was specifically trying to get at) and that averaging temperatures is just a very crude approach (taken presumably mainly in order to summarise the situation in a single 'alarming' number for ecotard propaganda purposes).

In short, averaging temperatures is a pretty crap way of expressing the energy flows, but given that one is going to do it then one would still want that (almost meaningless) average to be calculated correctly. My question was focused on this latter aspect as I suspect it isn't.

If you don't mind I'd like to come back on this. I intend to take a really simple 'toy' model to illustrate what (I think) I perceive as the essence of the problem. However, since I haven't attempted any formulation or calculation yet I might find that, when I do, my instinct about this is just plain nuts and I'm having a dumbarse senior moment.

Right now though, I'm pushed for time. On top of that my wife has decided to get on my case so I'm at DEFCON 2! :)